Scalar Fields->E Ratio provides a mesh quality measure for surface mesh elements, where 0 is worst (flat) and 1 is best (perfect regular element). For volume mesh quality the equivalent is Scalar Fields->Vol Ratio. To visualize the mesh elements see "View a Mesh".

The surface mesh is the primary means by which you indirectly control the volume mesh quality. Poor surface mesh quality leads directly to poor volume mesh quality. Hence, you need to focus on a good surface mesh. The higher the lowest E Ratio value the more likely you'll create a good volume mesh.

It's not so much absolute mesh quality values that determine whether a mesh will provide an accurate flow solution, but where poor mesh quality is situated. If there are a few randomly scattered poor surface or volume elements, e.g., between size transitions then that is likely OK. However, if you have a cluster of poor surface elements, e.g., severely stretched elements along a sliver face, then that will likely lead to a cluster of poor volume elements causing a simulation to fail or not converge.

For a failed simulation there are often unrealistic field values, e.g., velocity magnitude in the 100s when your reference value was 10, and you are likely to find those values clustered in poor mesh regions - another sign you need to improve/modify the mesh in that region. Note it may require a geometry change to improve the mesh, e.g., join faces to remove sliver faces.

If you are importing grids with highly stretched cells to resolve boundary layers then these metrics are not valid, instead use the metrics in the external software to evaluate the mesh.